Explanation Given: Let Δ f = f ( 5 + h ) − f ( 5 ) , where f ( x ) = x 2 . Formula used: Linear approximation of Δ f : If f is differentiable at x = a and Δ x is small then Δ f ≈ f ′ ( a ) Δ x Where Δ f = f ( a + Δ x ) − f ( a ) . Calculation: Let f ( x ) = x 2 . Also, Δ f = f ( 5 + h ) − f ( 5 )

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 4.1, Problem 73E

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Show that E=|Δf−f′(5)h| satisfy E≤12Kh2 with k=2.

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Chapter 4.1, Problem 72E

Chapter 4.1, Problem 74E

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Chapter 4 Solutions

Calculus: Early Transcendentals

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Show that E = | Δ f − f ′ ( 5 ) h | satisfy E ≤ 1 2 K h 2 with k = 2 .

Solution Summary: The author shows that E=left|Delta f-fprime (5)h right| satisfy with k=2.

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Show that E=|Δf−f′(5)h| satisfy E≤12Kh2 with k=2.

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Chapter 4 Solutions